How to use bl_label inside an operator?
You define bl_label inside the operator's code as a variable so after that you can reference it as any other variable inside the operator. It would be self.bl_label:

import bpy

class SimpleOperator(bpy.types.Operator):
    """Tooltip"""
    bl_idname = "object.simple_operator"
    bl_label = "Simple Object Operator"

    @classmethod
    def poll(cls, context):
        return True

    def execute(self, context):
        print(self.bl_label)
        return {'FINISHED'}

def register():
    bpy.utils.register_class(SimpleOperator)

def unregister():
    bpy.utils.unregister_class(SimpleOperator)

if __name__ == "__main__": 
    register()

    # test call
    bpy.ops.object.simple_operator()